This paper argues that the bridges and tails seen in some multiple galaxies are just tidal relics of close encounters. These consequences of the brief but violent tidal forces are here studied in a deliberately simple-minded fashion: Each encounter is considered to involve only two galaxies and to be roughly parabolic; each galaxy is idealized as just a disk of noninteracting test particles which initially orbit a central mass point. As shown here, the two-sided distortions provoked by gravity alone in such circumstances can indeed evolve kinematically into some remarkably narrow and elongated features: (i) After a relatively direct passage of a small companion, the outer portions of the primary disk often deform both into a near-side spiral arm or "bridge" extending toward this satellite, and into a far-side "counterarm." (ii) A similar encounter with an equal or more massive partner results typically in a long and curving "tail" of escaping debris from the far side of the victim disk, and in an avalanche of near-side particles, most of which are captured by the satellite. Besides extensive pictorial surveys of such tidal damage, this paper offers reconstructions of the orbits and outer shapes of four specific interacting pairs: Arp 295, M51 + NOC 5195, NGC 4676, and NOC 4038/9. Those models can be found in the fairly self-explanatory figures 19, 21, 22, and 23. Also discussed are some closely related issues of eccentric bound orbits, orbital decay, accretion, and forced spiral waves.